HW2 - finance, portfolio management, MM DCF WACC, Valuation CFC - FCFE, Equity, Financial PDF

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Homework II 1. R = 0.04 + 0.2 σ This is a classical Capital Market Line that has risk-free rate of 0.04. An one unit increase in standard deviation causes 0.2 increase in expected return. a. Risk Free rate is 0.04 ( 4% ) meaning that if the standard deviation is zero, we get 4% increase. Furthermore, with increasing standard deviation, an investor wants more return. In this equation, if the standard deviation is zero, then the investor gets 4% return (Risk-free rate). If the standard deviation is increased by 1 unit then the investor expects 0.2 unit more return.

b. If the standard deviation 16%, the expected return is: R = 0.04 + 0.2 * 0.16 = 0.04 + 0.032 = 0.072 = 7.2%

c. If the expected return is 12%, the standard deviation should be: R = 0.12 R = 0.04 + 0.2 σ 0.12 = 0.04 + 0.2 σ σ = 0.40 = 40% d. If 30YTL is invested in the risk free rate and 70YTL in the market portfolio: 30 YTL * Risk Free Rate = 30 YTL * 4% = 1.2 YTL 70 YTL in the market portfolio 70 YTL * Market Portfolio Expected Return Rate R = 0.04 + 0.2 * 0.16 = 0.04 + 0.032 = 0.072 = 7.2%

So, 70 YTL * 7.2% = 5.04 YTL Total return expected at the end of the year is: = 1.2 YTL + 5.04 YTL = 6.24 YTL

e. Market standard deviation is 16%. So, the expected return is R = 0.04 + 0.2 * 0.16 = 7.2% Therefore, it impossible to reach 112 payoff even if we invest all of our 100 YTL to market portfolio. ( The payoff will be 7.2)

2. The economy is normally distributed with expected return of 7.2%. The standard deviation is 0.16. If we invest 100 YTL, the expected payoff is will be 107.2 YTL. The distribution is normal. So, The probability that the payoff will be more than 107.2 can be calculated from: (107.2 -107.2) / 0.16 = 0 – From t-table, it is 50%.

3. There are two stocks and their correlation is 1/3. There is also a risk-free asset. Addionally, CAPM is satisfied.

a. Expected Return of the market is the weighted average of the two stocks. Here, in the question number of shares and the prices are given. So, the total value of stocks are: A --- 100* $ 1.5 = $ 150 B --- 150 * $ 2.0 =$ 300 The value weight of A is half of the stock B. Weight of A * A’s Return + Weight of B * B’s Return (1 * 15% +2 * 12%) /3 = 13%  The expected return on the market.

b.

Standard deviation of the two stocks are:

Weight1^2 * std1^2 + Weight2^2 * std2^2 + 2 * Weight1 * Weight2 * Covariance (stock1, stock2) The weights can be used as 1 and 2 respectively and the covariance of stocks can be calculated from their standard deviations and correlation coefficient. Covariance (stock1, stock2) = 1/3 * 0.15 * 0.09 = 0.0045 Standard deviation of the market portfolio is: = (0.4^2* 0.0225 + 0.6^2* 0.0081 + 2 * 1* 2 *0.0045)^1/2 = 0.09317 = 9.3% c. Beta can be calculated with the formulation that Covariance of the stock and market / market variance, so: Market variance is calculated above ( it is 0.093^2) Covariance is: (correlation of stock and the market) * standard deviation of stock A * standard deviation of the market (0.15/0.13) * 0.15 * 0.093 = 0.016 So, beta of the stock A is 0.016 / 0.093^2 = 1.86

d. With using the CAPM formula, risk free rate can be calculated. E(return) = rf + beta *(E(Mark.Ret – rf)) 0.15 = rf + 1.86 * (0.13 – rf ) So, rf = 10.69% e. The risk of the individual stock (Var) = portfolio risk ( Cov ) + diversifiable risk For stock A : 0.15 = 0.016 + diversifiable risk diversifiable risk = 13.4% For Stock B: 0.09 = 0.008 + diversifiable risk diversifiable risk = 8.2%...